Interest Rate Option Pricing With Volatility Humps

This paper develops a simple model for pricing interest rate options. Analytical solutiorls are developed for European claims and extremely efficient algorithms exist for tile pricing of American opciolls. T h e interest rate claims are priced in the Heath-Jarrow-klorto~i paradigm, and hence illcorporate full information on the term structure. T h e volatility. structure for forward rates is humped, and includes as a special case the exponentially dampened volatility structure used in tile Generalized Vasicek model. T h e structure of volatilities is captured without using time varying parameters. As a result, the volatility structure is stat iollav. I t is not possible to have all ttle above properties hold in a Heath Jarrow Morton model with a single s t a t e variable. I t is show11 t h a t the full dvliarnics of the term structure can, however, be captured by a three s ta te rCIarkovia11 system. As a result, simple path reconecting lattices cannot be constructed to price American claims. Nonetheless, we provide extremely efficient lattice based algorithms for pricing claims, which rely on carrying small matrices of information a t each node. Empirical support for the models developed zre provided.